[15.04] Dynamical evolution of comet nucleus rotation

The rotational dynamics of outgassing cometary nuclei are
investigated analytically. We develop a general theory for
the evolution of a comet nucleus' rotation state using
averaging theory and assuming that the outgassing torques
are a function of solar insolation and heliocentric
distance. The resulting solutions are a function of the
nucleus inertia ellipsoid, its outgassing properties, its
heliocentric orbit, and the assumed distribution of active
regions on its surface.

We find that the long-term evolution of the comet nucleus
rotation is a strong function of the distribution of active
regions over its surface. In particular, we find that nuclei
with nearly axisymmetric inertia ellipsoids and a uniformly
active surface will tend towards a rotation state that has a
nutation angle of ~ 55 degrees and its angular momentum
perpendicular to the sun-perihelion direction. If such a
comet nucleus has only one isolated active region, it will
tend towards a zero nutation angle with its approximate
symmetry axis and rotational angular momentum aligned
parallel to the sun-perihelion direction.

In the general case for an inertia ellipsoid that is not
close to being axisymmetric we find a much richer set of
possible steady-state solutions that are stable, ranging
from rotation about the maximum moment of the inertia axis,
to SAM and LAM non-principal axis rotation states. The
resulting stable rotation states are a strong function of
outgassing activity distribution, which we show using a
simplified model of the comet Halley nucleus. Also, we
demonstrate that comet Borrely observations are consistent
with a stable rotation state.

Our results can be used to discriminate between competing
theories of comet outgassing based on a nucelus' rotation
state. They also allow for a range of plausible a
priori constraints to be placed on a comet's rotation state
to aid in the interpretation of its outgassing structure.

This work was supported by the NASA JURRISS program under
Grant NAG5-8715. AIN, AAV, and VVS acknowledge support from
Russian Foundation for Basic Researches via Grants
00-01-00538 and 00-00-00174 respectively. Also they
acknowledge support from INTAS via Grant 00-221. DJS
acknowledges support from the PG&G program via Grant
NAG5-9017.